Lines and Angles Class 7 Worksheet

Name: __________________________
Date: __________________________
Class: 7

Instructions

Answer all questions. Show your working where necessary.

A. Basic Concepts

1. A line has ______ endpoints.
2. A line segment has ______ endpoints.
3. A ray has ______ endpoint.
4. An angle measuring (90^\circ) is called a __________ angle.
5. An angle measuring (180^\circ) is called a __________ angle.
6. An angle measuring less than (90^\circ) is called an __________ angle.
7. An angle measuring more than (90^\circ) but less than (180^\circ) is called an __________ angle.
8. Two angles whose sum is (90^\circ) are called __________ angles.
9. Two angles whose sum is (180^\circ) are called __________ angles.
10. Two lines that meet at (90^\circ) are called __________ lines.

B. Name the Type of Angle

11. (35^\circ) = __________________
12. (90^\circ) = __________________
13. (125^\circ) = __________________
14. (180^\circ) = __________________
15. (72^\circ) = __________________
16. (145^\circ) = __________________
17. (360^\circ) = __________________
18. (89^\circ) = __________________

C. Find the Missing Angle

19. Two complementary angles are (35^\circ) and (x^\circ). Find (x).
20. Two complementary angles are (48^\circ) and (x^\circ). Find (x).
21. Two supplementary angles are (65^\circ) and (x^\circ). Find (x).
22. Two supplementary angles are (112^\circ) and (x^\circ). Find (x).
23. One angle on a straight line is (75^\circ). Find the other angle.
24. One angle on a straight line is (143^\circ). Find the other angle.
25. Two angles are vertically opposite. One angle is (58^\circ). Find the other.
26. Two vertically opposite angles are (x^\circ) and (82^\circ). Find (x).

D. Intersecting Lines

27. When two lines intersect, vertically opposite angles are __________.
28. If one angle formed by two intersecting lines is (70^\circ), what is the vertically opposite angle?
29. If one angle is (110^\circ), what is its adjacent angle?
30. Two lines intersect and one angle is (45^\circ). Find the other three angles.
31. Two lines intersect. One angle is (125^\circ). Find the other three angles.
32. If two adjacent angles form a linear pair and one is (68^\circ), find the other.

E. Parallel Lines and a Transversal

Use the properties of parallel lines cut by a transversal.

33. Corresponding angles are __________ when two parallel lines are cut by a transversal.
34. Alternate interior angles are __________ when two parallel lines are cut by a transversal.
35. Co-interior angles are __________.
36. If a corresponding angle is (75^\circ), find its corresponding angle.
37. If an alternate interior angle is (110^\circ), find the other alternate interior angle.
38. If one co-interior angle is (65^\circ), find the other.
39. Two parallel lines are cut by a transversal. One angle is (120^\circ). How many of the eight angles measure (120^\circ)?
40. In the same figure, how many angles measure (60^\circ)?

F. Find (x)

41. (x + 65^\circ = 180^\circ)
42. (x + 42^\circ = 90^\circ)
43. (x + 115^\circ = 180^\circ)
44. (x = 2(35^\circ))
45. (2x + 20^\circ = 90^\circ)
46. (3x + 30^\circ = 180^\circ)
47. (2x + 40^\circ = 180^\circ)
48. (x + 75^\circ = 180^\circ)
49. (4x = 120^\circ)
50. (3x + 15^\circ = 90^\circ)

G. True or False

51. A straight angle measures (180^\circ). ______
52. Vertically opposite angles are always equal. ______
53. Complementary angles always form a straight line. ______
54. Supplementary angles have a sum of (180^\circ). ______
55. Perpendicular lines meet at (90^\circ). ______
56. A right angle is greater than (90^\circ). ______
57. Alternate interior angles are equal for parallel lines. ______
58. Co-interior angles have a sum of (180^\circ). ______

H. Word Problems

59. Two angles form a linear pair. One angle is (85^\circ). Find the other angle.
60. Two complementary angles differ by (20^\circ). Find both angles.
61. Two supplementary angles are in the ratio (2:1). Find both angles.
62. Two vertically opposite angles are represented by (3x+10^\circ) and (100^\circ). Find (x).
63. Two co-interior angles are (4x^\circ) and (2x^\circ). Find (x).
64. A transversal crosses two parallel lines. One of the acute angles is (55^\circ). Find the obtuse angles.
65. An angle is (30^\circ) less than its supplementary angle. Find both angles.

I. Challenge Questions

66. Three angles around a point are (80^\circ), (120^\circ), and (x^\circ). Find (x).
67. Four angles around a point are (70^\circ), (90^\circ), (80^\circ), and (x^\circ). Find (x).
68. An angle is twice its complementary angle. Find both angles.
69. An angle is three times its supplementary angle. Find both angles.
70. Two parallel lines are cut by a transversal. One angle is (3x+20^\circ), and its corresponding angle is (5x-40^\circ). Find (x) and the angle.

Answer Key

A

1. 0
2. 2
3. 1
4. Right
5. Straight
6. Acute
7. Obtuse
8. Complementary
9. Supplementary
10. Perpendicular

B

11. Acute
12. Right
13. Obtuse
14. Straight
15. Acute
16. Obtuse
17. Complete
18. Acute

C

19. (55^\circ)
20. (42^\circ)
21. (115^\circ)
22. (68^\circ)
23. (105^\circ)
24. (37^\circ)
25. (58^\circ)
26. (82^\circ)

D

27. Equal
28. (70^\circ)
29. (70^\circ)
30. (45^\circ, 135^\circ, 45^\circ, 135^\circ)
31. (125^\circ, 55^\circ, 125^\circ, 55^\circ)
32. (112^\circ)

E

33. Equal
34. Equal
35. (180^\circ)
36. (75^\circ)
37. (110^\circ)
38. (115^\circ)
39. 4
40. 4

F

41. (115^\circ)
42. (48^\circ)
43. (65^\circ)
44. (70^\circ)
45. (35^\circ)
46. (50^\circ)
47. (70^\circ)
48. (105^\circ)
49. (30^\circ)
50. (25^\circ)

G

51. True
52. True
53. False
54. True
55. True
56. False
57. True
58. True

H

59. (95^\circ)
60. (35^\circ, 55^\circ)
61. (120^\circ, 60^\circ)
62. (x=30)
63. (x=30)
64. (125^\circ)
65. (75^\circ, 105^\circ)

I

66. (160^\circ)
67. (120^\circ)
68. (30^\circ, 60^\circ)
69. (135^\circ, 45^\circ)
70. (x=30), angle (=110^\circ)